## Singmaster Moves

Professor David Singmaster, an English mathematician, was one of the first to investigate Rubik's Cube™ and its relationship to the branch of mathematics known as Group Theory. In his book, Notes on Rubik's 'Magic Cube', Fifth Edition, published in 1980, he sets out a way of describing sequences of cube moves briefly. Mathematicians call this a notation and Singmaster's Notation is now widely used internationally in books and on websites when discussing problems and solutions in Rubik's Cube™ puzzles. For example, see the Wikipedia article and its links on the subject of Rubik's Cube™.

The Kubrick program uses a modified form of Singmaster Notation to display all moves, by whatever method they are made, using an area of the toolbar. It also allows moves to be entered from the keyboard in Singmaster Notation. The notation has been modified for use on larger cubes, bricks and mats than the original size 3 cube and to allow convenient entry from the keyboard, without clashing with Kubrick shortcuts or other actions.

Briefly, Singmaster imagines that you are looking at the cube from slightly above and to the right of it, exactly as in the standard Front View of Kubrick. You can see three faces at the top, front and right of the cube and these Singmaster has called (in English) Up, Front and Right, or U, F and R for short. The three faces you cannot see, which are on the Back View in Kubrick, are at the bottom, back and left of the cube and Singmaster calls these (in English) Down, Back and Left, or D, B and L for short. Singmaster uses U and D for the top and bottom faces because B is reserved for the back face.

This is all summarised in the table below: now to the moves. A single letter or keystroke from UFRDBL represents a clockwise move of that face through a right angle (90 degrees) for a square face or through 180 degrees for a rectangular face (as on a brick or mat). Here is where it gets tricky.

Clockwise means clockwise when you are looking directly at that face. That is easy enough with the UFR faces you can see, but the faces you cannot see appear to move anti-clockwise when you use DBL moves. That is because you are looking at them from behind. On Kubrick's Back View, the DBL moves will be seen to go clockwise, as expected. Rather than trying to imagine yourself looking at the back of the cube when making DBL moves, it might be easier to think of them going anti-clockwise in the normal Front View.

Singmaster Notation (Modified)
KeyMeaning
RRight face. In English, R is for Right.
LLeft face. In English, L is for Left.
UUp or top face. In English, U is for Up.
DDown or bottom face. In English, D is for Down.
FFront face. In English, F is for Front.
BBack face. In English, B is for Back.
'Suffix for a reverse or anti-clockwise move. R' is the reverse of R.
2Suffix for double move. R2 rotates R twice.
+Suffix for two-face move. R+ is RL' in another form.
-Suffix for anti-two-face move. R- is RL in another form.
.Prefix for inner-slice move. .R is one step in from the R face.
CPrefix for whole-cube move. In English, C is for Cube.

Singmaster uses a letter followed by an apostrophe to represent an anti-clockwise or reverse move of a face. Mathematicians would say F' as F prime or F dash and it indicates an anti-clockwise move of the front face.

Kubrick cannot tell if you are going to type an apostrophe, another letter or some other symbol after a letter, so it will not make a clockwise move of a face immediately after you type the letter. You can force Kubrick to move by hitting the Return or Enter key. You can also use the space bar and it will leave a space in the display of moves, allowing you to separate groups of moves for readability.

On cubes, bricks or mats of size 3 or more, you might wish to move an inner slice, rather than a face. To do this, type one or more periods or dots before the face letter. For example, ..F moves the slice that is two layers behind the front face and ..B would move the slice two layers in front of the back face, assuming there are 5 or 6 layers that can move. The reverse of those moves would be ..F' and ..B'.

Finally, the C prefix moves the whole cube in the same way as a face. For example, CF moves the cube clockwise along with the front face and CF' moves it anti-clockwise.

If you have previously rotated the cube by hand, using the right mouse button, and you then make a Singmaster or other keyboard move, the cube will be realigned automatically to standard UFR view and some C moves will be generated and displayed. This ensures that you and Kubrick have the same idea of top, front and right. Similar moves are generated when you use the MoveRealign Cube menu item or the Home icon on the toolbar.